Pythagorean Cup — Greedy Cup / Cup of Justice (parametric)

A working Pythagorean cup — also called the greedy cup or *cup of

justice* (κύλιξ τῆς δικαιοσύνης). Attributed to Pythagoras of Samos

around the 6th century BC, it's a vessel that rewards moderation: fill

it modestly and it holds liquid like any cup; fill it past the hidden

"greedy line" and the entire contents siphon out through a hole in the

bottom — usually into the user's lap.

How it works: inside the cup, a hollow column rises from the floor.

Two parallel vertical bores run through the column. One (the riser)

is open at the cup floor and runs up to a bend near the top. The other

(the descender) starts at that bend and runs down through the

underside of the cup to a small drain hole. A horizontal channel at

the top connects them — the inverted-U "siphon bend".

• Fill below the bend → cup-side fluid level matches riser-side level

•   (communicating vessels). Bend stays dry. No flow.

• - Fill above the bend → fluid spills over the bend into the descender.

•   Once the descender is primed, gravity siphons the entire cup out

•   through the bottom hole until air enters the riser at the floor.

Working dimensions (default): Ø 50 mm × 60 mm tall. Greedy line at

~80 % fill (z = 48 mm). Walls 1.6 mm (4 perimeters at 0.4 mm nozzle).

Drain hole Ø 4 mm.

Parametric — change the size in one line. The included .scad

exposes cup_d(diameter) and cup_h(height) as top-level parameters.

Want a tall narrow shot-cup or a wide goblet? Edit those two numbers

and re-render. The siphon bend, bores, drain, and column geometry all

follow automatically; the greedy line stays at ~80 % of cup_h.

Print notes (Bambu P2S, 0.4 mm nozzle, 0.2 mm layer, PLA tested):

• Print upright, bottom face on bed. No supports.

• - The horizontal siphon bend is a 4–5 mm Ø 4 mm bridge — Bambu prints

•   cleanly at this scale.

• - Use waterproof / food-safe filament if you intend to actually drink

•   from it. PLA holds water for casual prank use; for repeated use

•   consider sealing with a food-safe epoxy or printing in PETG.

Tested working — verified with the default dimensions: water below

the bend is held; water above the bend siphons out completely through

the drain hole. Classic dinner-party trick / physics demo.